Health insurance markets with regulated premiums typically include risk adjustment (RA) to mitigate selection incentives. Even the most sophisticated RA models, however, tend to undercompensate (overcompensate) insurers for people in poor (good) health. One reason RA models are imperfect is that some predictors cannot serve as risk adjustor because they are not available for the entire population. This paper applies an indirect method to exploit such predictive information: constrained regression. Our focus is on the Netherlands where morbidity data from general practitioners (GPs) are available for only around 10 percent of the population. We combine this incomplete sample with complete data (N=16.7 million) on spending and risk adjustors. In a first step, we find that GP morbidity data are predictive net of the Dutch RA model. In a second step, we use the GP morbidity data to impose constraints on the coefficients of the RA model. This results in more RA funds being sent to undercompensated groups. Using a split-sample approach, we simulate two constrained regression models and compare the outcomes to those of an unconstrained model. Our findings indicate that constrained regression can be a useful tool to exploit predictive information that is available for only a sample of the population.

中文翻译：

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使用约束回归在风险调整中利用不完整的信息

具有规定保费的健康保险市场通常包括风险调整（RA），以减轻选择动机。但是，即使是最复杂的RA模型，对于健康状况欠佳（良好）的人，保险公司也往往补偿不足（过度补偿）。RA模型不完善的原因之一是，某些预测变量不能用作风险调整因子，因为它们不适用于整个人群。本文采用一种间接方法来利用此类预测信息：约束回归。我们的重点是在荷兰，那里只有大约10％的人口可从全科医生（GPs）获得发病率数据。我们将这个不完整的样本与有关支出和风险调整因素的完整数据（N = 1670万）结合在一起。第一步，我们发现GP发病率数据是Dutch RA模型的预测网。第二步 我们使用GP发病率数据对RA模型的系数施加约束。这导致更多的RA资金被发送到补偿不足的群体。使用拆分样本方法，我们模拟了两个约束回归模型，并将结果与​​非约束模型的结果进行了比较。我们的研究结果表明，约束回归可能是开发仅适用于一部分样本的预测信息的有用工具。